$-1\dfrac{3}{5} \div \dfrac{5}{-6} = $
Let's start by converting the mixed number to a fraction. $\phantom{=}-1\dfrac{3}{5} \div \dfrac{5}{-6}$ $-\dfrac{8}{5} \div \dfrac{5}{-6}$ $=-\dfrac{8}{5} \cdot \dfrac{-6}{5}~~~~~~~\text{multiply by the reciprocal}$ $=-\dfrac{-48}{25}$ $=\dfrac{48}{25} \text{ or }1\dfrac{23}{25}$